Chapter 4
Where Does the Wave Equation Come
From?
Motion is always motion in reference to something, i.e. a reference system (reference
frame) where the observers sit, watch and measure. A mass m moves relative to the
reference system of an observer. The observer is per definition considered as resting.
If we take two observers moving against each other in two different reference systems,
each observer will come to a different conclusion about the motion of the mass m. I
sit at my desk on which a mass m is lying. A colleague swivels on a revolving chair
next to me. He sees that the mass m, the desk and I are orbiting around him; see
Fig. 4.1.
Are both frames, myself sitting at a desk and my colleague on his revolving chair
equal to one another? Well, after a few minutes my colleague should start to get
dizzy, whereas I do not. If I were more sensitive, I should also get dizzy, because
of the rotation of the earth. If my perceptiveness was far greater, the orbiting of
the earth around the sun and perhaps the accelerated motion of the complete solar
system could cause me dizziness. Special systems of reference are those systems
that principally do not cause ‘dizziness’. These special systems are called inertial
systems or inertial frames.
What is meant is that the motion of an object in such systems is defined by its
inertia, its persistence to remain motionless or to keep moving at a uniform velocity
in the same direction as long as the object is not influenced by any physical force.
We will assume for the following discussion that we are inside one of these inertial
frames. My desk is an appropriate approximation for this purpose. A colleague sitting
in a train moving past me at a constant speed is then also inside an inertial frame.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_4
19
Where Does the Wave Equation Come
From?
Motion is always motion in reference to something, i.e. a reference system (reference
frame) where the observers sit, watch and measure. A mass m moves relative to the
reference system of an observer. The observer is per definition considered as resting.
If we take two observers moving against each other in two different reference systems,
each observer will come to a different conclusion about the motion of the mass m. I
sit at my desk on which a mass m is lying. A colleague swivels on a revolving chair
next to me. He sees that the mass m, the desk and I are orbiting around him; see
Fig. 4.1.
Are both frames, myself sitting at a desk and my colleague on his revolving chair
equal to one another? Well, after a few minutes my colleague should start to get
dizzy, whereas I do not. If I were more sensitive, I should also get dizzy, because
of the rotation of the earth. If my perceptiveness was far greater, the orbiting of
the earth around the sun and perhaps the accelerated motion of the complete solar
system could cause me dizziness. Special systems of reference are those systems
that principally do not cause ‘dizziness’. These special systems are called inertial
systems or inertial frames.
What is meant is that the motion of an object in such systems is defined by its
inertia, its persistence to remain motionless or to keep moving at a uniform velocity
in the same direction as long as the object is not influenced by any physical force.
We will assume for the following discussion that we are inside one of these inertial
frames. My desk is an appropriate approximation for this purpose. A colleague sitting
in a train moving past me at a constant speed is then also inside an inertial frame.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_4
19